In 1987, Ito, Saito and Nishizeki proposed a secret sharing scheme realizing general access structures, called the multiple assignment secret sharing scheme (MASSS). In this paper, we propose new MASSS's which are perfect secret sharing schemes and include Shamir's (k,n)-threshold schemes as a special case. Furthermore, the proposed schemes are more efficient than the original MASSS from the viewpoint of the number of shares distributed to each participant.